Method for determining deviations between coordinate systems of different technical systems

ABSTRACT

Method for determining deviations between coordinate systems of different technical systems, comprising the steps of determining a coordinate position of a reference feature of a test object in the coordinate system (u,v) of a first of the technical systems, the attachment of at least one test feature to the test object, with the test feature being attached in the coordinate system of a second of the technical systems at a coordinate position that is determined in dependence on the determined coordinate position of the reference feature, the determination of a coordinate position of at least one test feature and/or at least one feature derived from it in the coordinate system (u,v) of the first technical system, and determination of deviations between the coordinate systems of the first and second technical system, at least on the basis of: (a) the determined coordinate position of at least one test feature and/or of at least one feature derived from it in the coordinate system (u,v) of the first technical system and (b) the coordinate position of the reference feature in the coordinate system (u,v) of the first technical system.

This is a United States national phase application of co-pendinginternational application number PCT/EP2010/000920 filed on Feb. 15,2010, the disclosure of which is incorporated herein by reference.

TECHNICAL FIELD

The invention relates to a method for determining deviations betweencoordinate systems of different technical systems.

BACKGROUND

Technical systems often operate with coordinate systems which theyrequire for determining the position of occurring events, of actions tobe carried out and/or of objects in motion or at rest. Sensor systemsthat detect the location of an event or of an object in a single- ormulti-dimensional coordinate system, are examples of this. Such sensorsystems can, for example, be camera-based and be configured as a motiontracking system. Such motion tracking systems are used to recognize andtrack the (changeable) position of moving objects.

One example of a motion tracking system especially considered within theframework of the invention is a so-called eye tracker, by which eyemovements can be detected. Use of eye trackers is current practice inlaser-surgery ophthalmology, thus processing of the human eye by meansof laser radiation for the purpose of eliminating or at least reducingincorrect functions or pathology of the eye.

Without mechanical fixing, the human eye never is totally still, butrather even when taking aim at a specific fixation target it continuesto make smaller and larger movements (such as the saccades), andtherefore with various techniques of eye treatment by laser surgery, aneye tracker is used, to detect movements of the eye to be treated, anddepending on the detected eye position, to guide the treating laser. Asan example in this regard, especially refractive laser treatment isespecially named, in which corneal tissue is ablated (i.e. removed fromthe surface) using laser radiation in the UV wavelength range, in thisway to reform the corneal front surface and by this means to alter therefractive properties of the cornea. One example of such a refractivetechnique is so-called LASIK (Laser In Situ Keratomileusis), in which atfirst by means of a mechanical microkeratom or by means of femtosecondlaser radiation, laser radiation cuts out from the cornea a smallcovering disk customarily designated in the technical world as a flap.The flap is not totally separated from the corner, but still hangs in ahinge area on the remaining corneal tissue. The flap is then pivoted tothe side and the corneal material thus revealed is subjected to anablating laser treatment. Then the flap is pivoted back again. Becausethe outer epithelium layer of the cornea is only slightly damaged inthis method, the wound heals relatively quickly.

Laser devices that generate a positionally controllable laser beam forprocessing a material, are another example of technical systems thatoperate with a coordinate system. The ablation positions of the laserbeam, thus those positions to which the laser beam is to be directed,can be defined by coordinate positions in the coordination system of thelaser device. With laser devices that generate pulsed laser radiation,every coordinate position can be assigned to a single laser pulse or agroup of laser pulses.

SUMMARY OF EXAMPLE EMBODIMENTS

The above reference to using an eye tracker in laser surgery treatmentof the human eye makes it already clear that in practice solutions oftenoccur in which multiple technical systems, each with its own coordinatesystem, operate together. If one of the technical systems transmitscoordinate values that it determined or fixed with reference to its owncoordinate system, to another technical system, that receives thesetransmitted coordinate values to determine the coordinate positions ofan action to be taken in its coordinate system, for example, problemscan arise if the coordinate systems of the two technical systems are notmutually adjusted. It is readily imagined that a certain point in aspace in a coordinate system of the one technical system can havecoordinate values different from the same space point in the coordinatesystem of the other technical system. This can for example be at adifferent place of the coordinate center of the two coordinate systemsin space. The two coordinate systems can also be distorted relative toeach other. Another cause can be in an a different scaling of thecoordinate axes, i.e., the same nominal coordinate values along an axiscan be at a different distance from the coordinate origin from that inthe other coordinate system.

If the coordinate systems of different technical systems operating inconcert with each other are not spatially identical to each other, forproper functioning of the cooperation at minimum it is necessary to haveprecise knowledge about the differing spatial position and/or thediffering scaling of the coordinate systems, to be able to convert acoordinate position from one of the coordinate systems into acorresponding coordinate position of another coordinate system. Oftenthis knowledge is not present and must be laboriously determined.

U.S. Pat. No. 4,134,681 is concerned with determining the relativeorientation of two physical systems. For two beam vectors that forexample indicate the direction of a laser beam, the particular vectordirection is determined in the coordinate systems of the two physicalsystems, so that altogether four directional vectors are obtained, twofor each coordinate system. From these four directional vectors, thenthe relative orientation of the two coordinate systems, and thus of thetwo physical systems, is determined.

The task of the invention is to indicate a simple method, and, aboveall, one that is accessible to automated implementation, for determiningdeviations between coordinate systems of different technical systems.

To solve this problem, in agreement with the features of claim 1, theinvention provides a method for determining the deviations betweencoordinate systems of different technical systems, comprising:

-   -   determination of a coordinate position of a reference feature of        a test object in the coordinate system of a first of the        technical systems,    -   attachment of at least one test feature to the test object, with        the test feature being attached in the coordinate system of a        second of the technical systems at a coordinate position that is        determined in dependence on the determined coordinate position        of the reference feature,    -   determination of a coordinate position of at least one test        feature and/or at least one feature derived from it in the        coordinate system of the first technical system, and    -   determination of deviations between the coordinate systems of        the first and second technical system, at least on the basis of:

(a) the determined coordinate position of at least one test featureand/or of at least one feature derived from it in the coordinate systemof the first technical system, and

(b) the coordinate position of the reference feature in the coordinatesystem of the first technical system.

With the invention-specific solution, in one embodiment a test object isused that is provided with a reference pattern which can be detected bya first of the technical systems. The reference pattern can directlyform the reference feature. Alternatively, the reference pattern can beconfigured so that a reference feature can clearly be derived from it.For example, the reference feature can be the center (midpoint) of ageometric object serving as the reference pattern. Algorithms whichcompute the midpoint from a detected geometric form are known per se anddo not need to be explained in detail here. In any case, in a preferredembodiment, the first technical system is in a position, based on thedetected reference pattern, to determine the coordinate position of thereference feature in its coordinate system (i.e., in the coordinatesystem of the first technical system).

The coordinate position thus determined (depicted by one or morecoordinate values) is then transmitted by the first technical system toa second of the technical systems. The second technical system uses thetransmitted coordinate values of the reference feature as if they werecoordinate values of its own coordinate system (i.e., of the coordinatesystem of the second technical system), and in its coordinate systemdetermines the coordinate position for a test feature to be generated inaccordance with a preset generation rule depending on the transmittedcoordinate position of the reference feature. For example, for the testfeature, a generation rule can be preset that along at least one part ofthe coordinate axes of the coordinate system of the second technicalsystem it has a preset coordinate distance from the reference feature.Through such a generation rule, in the coordinate system of the secondtechnical system, the position of the test feature can clearly be setwith reference to the position of the reference feature.

In a preferred embodiment, the second technical system then attaches acoordinate position determined in the above manner, dependent on thecoordinate position of the reference feature, to the test feature. Ifmultiple test features are to be attached, the second technical systemacts in a corresponding manner for each of the test features.

In a following step, the test object with the reference pattern and theattached test features is again investigated by the first technicalsystem. The first technical system determines which coordinate positionat least one test feature and/or a feature derived from it has in thecoordinate system of the first technical system. Based on this, now oneor more deviations can be determined within the coordinate system of thefirst technical system. Preferably at least one displacement vector isdetermined, by which the coordinate system of the second technicalsystem is spatially displaced vis-à-vis the coordinate system of thefirst technical system, and/or a relative twisting is determined betweenthe coordinate systems of the two technical systems and/or scalingdifferences are determined between the coordinate systems of the twotechnical systems.

The deviations determined can be converted into one or more correctionfactors that are consulted by the second technical system in lateroperations for correction of any coordinate positions that it receivesas transmitted from the first technical system. In this way, successfuladjustment is made in the coordinate systems of the two technicalsystems.

In one preferred embodiment, as part of the invention-specific method,multiple test features are attached to different locations of the testobject. At least one part of the test features can be attached in apolygon arrangement, for example a rectangular arrangement, round aboutthe reference feature on the test object. Then as a derived feature, apolygonal center of the test features arranged as a polygon can bedetermined, and in the coordinate system of the first technical system adeviation can be determined between the coordinate position of thereference feature and the coordinate position of the polygon center.

According to another embodiment, the deviations between the coordinatesystems of the first and second technical systems are further determinedon the basis of a target coordinate position of at least one featureamong the testing and derived features in the coordinate system of thefirst technical system. The target coordinate position of a test featurecan be determined, for example, by application of thepreviously-mentioned generation rule in the coordinate system of thefirst technical system. If for example the generation rule for the testfeature makes provision for a preset x-distance and a preset y-distanceof the reference feature along two axes x, y of the coordinate system ofthe second technical system, then the target coordinate position of thetext feature in the coordinate system of the first technical system canbe determined by these same nominal (numerical) coordinate distancesbeing applied to the determined coordinate position of the referencefeature.

According to a preferred embodiment form, the first technical systemcomprises a motion tracking device with a camera directed at the testobject, with the motion tracking device determining the coordinateposition of the reference feature and of at least one testing and/orderived feature in a first coordinate system.

The test object can bear a pattern, the center of which is determined bythe motion tracking device as the reference feature. The pattern(reference pattern) can for example be a flat pattern that is opticallycontrasted vis-à-vis the surrounding area. Optical contrast should existat least at the boundary of the reference pattern with the surroundingarea. It can be brought about at least in part by differing gray stagesor differing color tones of the pattern and of the surrounding area.Alternatively or additionally, it is possible to generate or amplify thecontrast between the reference pattern and the surrounding area, byhaving the two areas obtain differing surface treatments, or one of theareas obtaining a surface treatment while the other area remains withoutit. For example, the surrounding area of the reference pattern can beprovided with a network of printed points or lines, while the referencepattern remains patternless and is covered over its entire surface by aspecific gray or color tone.

In other respects it is not necessary that the reference pattern and/orthe surrounding area have only a single color. A color or gray-stagegradation can be implemented within the reference pattern and/or withinthe surrounding area.

The reference pattern can have a round outline, for example a circularor elliptical outline. In this way a two-dimensional projection of ahuman pupil can be simulated. The size of the reference pattern can atleast approximately correspond to a human pupil. In this case, thereference pattern represents a pupil model. This is appropriate in thatimage processing algorithms that compute the position of a pupil centerfrom a pictorially detected pupil of the eye, are known per se and canbe obtained on the market. A test object with such a pupil model isespecially suited therefore for application of the invention as part ofa device for laser surgery treatment of the human eye. It is readilyunderstood that non-round outline shapes of the reference pattern areequally possible, as long as it is ensured that the reference patternpossesses a clearly determinable center. Also, the reference patterndoes not have to correspond in size to a human pupil. It can be largeror smaller.

The second technical system preferably comprises a laser device whichapplies at least one test feature by means of a laser beam, especially apulsed laser beam, to the test object. The laser device uses a secondcoordinate system for positioning of the laser beam.

To be able to do good detection with an eye tracker or generally with acamera-based motion tracking device of the attached test feature, it isrecommended that for attachment of a test feature, the test object betreated with a laser beam so that there arises a local coloring and/orlocal cratering of the test object.

The at least one deviation determined is appropriately used forcorrection of coordinate data, which the second technical systemreceives as transmitted from the first technical system and which itneeds for its operation. The at least one deviation determined can beconverted into one or more suitable correction or calibration factures,which are applied to the coordinate data transmitted from the firsttechnical system.

The invention further relates to a test object for use in a method ofthe type mentioned above. The test object possesses a pattern thatstands out optically (reference pattern) and at least in one area aroundthe pattern is configured so that through local laser irradiation, testfeatures that stand out optically can be generated.

Preferably the pattern is an areal pattern which can model a human pupiland appears in a first color, while the test object appears in an areaaround the pattern in a second color. The second color is different fromthe first color. The term “color” here is to be broadly understood.Different colors can for example be implemented by different color tones(including gray) or by different gray stages or by differing brightnessvalues of a color tone.

According to one example, the first color can be printed on a substrateof the test object. In the area surrounding the reference pattern, thesubstrate can have a single colored layer with a color differing fromthe first color. By laser irradiation this colored layer (white, forexample) can then undergo color alteration, thus allowing the testfeatures to be perceptible. But it is also possible for the substrate inthe surrounding area to have multiple differing color layers one abovethe other, of which the uppermost (outermost) displays the second color,so that the test object appears in the surrounding area in the secondcolor. With laser irradiation, the second color can be bleached out ordisappear by some other means, through which the color layer lyingunderneath can be revealed. On the one hand this ensures that thereference pattern is easily recognized, and on the other hand, at leastone test pattern is easily recognized.

For example the test object is configured as a plate or sheet. It candisplay a piece of paper or cardboard, for example, which bears thepattern on its flat sides and is simultaneously configured there forgeneration of the test features. The piece of paper or cardboard can forexample be glued to a stable carrier plate made of metal or plastic, tomake the test object overall sufficiently stiff and robust.

In one variation, the test object can possess a curved (or generallythree-dimensional) surface, onto which the reference pattern is attachedand the test features can be attached. For example, this surface canmodel the front surface of a human eye. It then can be necessary foradjustment of the coordinate systems to additionally make allowance forthe curvature or curvature progression of the test object surface, toavoid any scaling errors.

Lastly the invention relates to a device for laser-surgeryophthalmology, comprising:

-   -   a laser device to make available a pulsed focused laser beam and        to direct same toward an eye to be treated, an eye tracker for        detecting eye movements, and    -   a control unit coupled with the eye tracker, which is furnished        to control the laser device in dependence on the detected eye        movement, wherein the control unit is additionally furnished        for:

(i) carrying out a method of the type mentioned above, to determinedeviations between a first coordinate system used by the eye tracker anda second coordinate system used by the laser device, and

(ii) to allow for determined deviations with the control of the laserdevice.

BRIEF DESCRIPTION OF THE DRAWINGS

In what follows, the invention will be further explained using theappended drawings. Shown are:

FIG. 1-an embodiment in a schematic block diagram of a device forlaser-surgery ophthalmology

FIG. 2-an example of spatial positions that differ from each other oftwo coordinate systems used in the device from FIG. 1

FIG. 3-an embodiment example of a test object usable for calibration ofthe device in FIG. 1.

DETAILED DESCRIPTION OF THE DRAWINGS

The device shown in FIG. 1, generally designated by 10 for laser-surgeryophthalmology, is set up to carry out corneal ablations of an eye 12 tobe treated. It comprises a laser source 14 which generates a pulsedlaser beam 16, that by means of a controllable deflection unit (scanner)18 is specifically deflectable in a plane normal to the beam direction,hereinafter named the x-y plane. Placed next to the scanner 18 is afocusing unit 20, which focuses the laser beam 16 on the eye 12 to betreated.

For ablative treatments, the wavelength of the output of laser source 14is in the ultraviolet range. For example, laser source 14 comprises anexcimer laser emitting at 193 nm.

The scanner 18 is formed for example in a manner known per se by a pairof galvanometrically controllable deflection mirrors. The focusing unit20 can be formed by a single lens or by a multi-lens system.

An electronic control unit 22 controls the laser source 14 and thescanner 18 in accordance with an ablation profile implemented by acontrol program, determined in advance for the patient. The ablationprofile indicates how much corneal material must be removed at whatlocation of the eye to be treated. Each laser pulse (shot) causes aspecific amount of material to be removed. The control program causes asmany laser pulses to be placed at each location in the ablation area asare needed to remove the desired material thickness. The ablationpositions are depicted by pairs of coordinates that relate to the twoaxes of a (rectangular) x-y coordinate system that sets the mentionedx-y plane. The pairs of coordinates indicate the coordinate distancefrom a center of the ablation profile (ablation center) that typicallyis defined in dependence on the pupil center of the eye 12 to betreated. Unavoidable movements of the eye 12 lead to continual changesin the position of the pupil center, and consequently of the ablationcenter in the x-y coordinate system.

For monitoring eye movements, the device 10 comprises an eye trackingdevice 24 designated for short as an eye tracker, which with a camera,for example, takes an infrared image of the eye 12 and especially theiris with the pupil, and by means of suitable image-processing softwarecomputes the position of the pupil center. However, the eye tracker 24does not operate with the same x-y coordinate system that the controlunit 22 and the scanner 18 operate with. Rather, it computes theposition of the pupil center in its own (rectangular) coordinate system,which for purposes of illustration is designated as a u-v coordinatesystem. In this u-v coordinate system, the eye tracker 24 indicates theposition of the pupil center in like manner through a pair ofcoordinates, thus a coordinate value for the u-axis and the v-axis.

The control unit 22 obtains from the eye tracker 24 the u-v coordinateposition of the pupil center and converts it into the corresponding x-ycoordinate position. With this it relies back to initially determinedcorrection information that represents any spatial position deviationsand any scaling deviations between the two coordinate systems. Thecorrection information can for example be implemented in the form of acorrection function or in the form of one or more correction factor tobe used multiplicatively or additively. From the position of the pupilcenter converted into x-y coordinates, the control unit 22 can thencompute the current position of the ablation center and appropriatelyguide the scanner.

Shown schematically in FIG. 2 are possible deviations between the x-ycoordinate system used by control unit 22 and scanner 18 and the u-vcoordinate system used by eye tracker 24. To better distinguish, the x-ycoordinate system is shown by continuous lines, while the u-v coordinatesystem is shown by dashed lines.

As a first deviation of the two coordinate systems in space, in theexample case of FIG. 2, a different position of the coordinate originsis perceived, thus the crossing points of the coordinate axes. Thisdiffering spatial position can be expressed by a displacement vector.

As a second deviation, in the example case of FIG. 2, a relativetwisting of the two coordinate systems is perceived. The measure of thistwisting can be indicated by an angular value.

A third deviation of the coordinate systems can consist in a differentscaling. To illustrate this situation, in FIG. 2 two coordinate valuesx₁, x₂ are identified on the x axis, which nominally correspond to twocoordinate values u₁, u₂ drawn in on the u axis. Nominal correspondencemeans that the coordinate values x₁ and u₁ are numerically equal and thecoordinate values x₂ and u₂ are also numerically equal.

True, it is easy to perceive that the coordinate value x₁ is at aconsiderably shorter distance from the center of the x-y coordinatesystem than the coordinate value u₁ is from the center of the u-vcoordinate system. In the same way, the distance of the coordinate valuex₂ from the center of the x-y coordinate system is smaller than thedistance the coordinate value u₂ has from the center of the u-vcoordinate system. If the numerical values of x₁ and u₁ agree and if thenumerical values of x₂ and u₂ agree, this means that the scaling of thex axis is different from the scaling of the u axis.

In a similar way, in FIG. 2 on the y axis a coordinate value y₁ is drawnin, which in regard to its numerical value corresponds to coordinatevalue v₁ drawn on the v axis. True, here also the distances of thecoordinate values v₁ from the center of the particular coordinate systemare different. Namely, the distance of coordinate value y₁ from thecenter of the x-y coordinate system is considerably greater than thedistance of coordinate value v₁ from the center of the u-v coordinatesystem. This also means a different scaling of the y axis in comparisonto the scaling of the v axis.

Such scaling deviations can exist for all the axes of the coordinatesystems, or for only a part of the axes.

Each of the explained three possible deviations results in points thatare described in the x-y coordinate system and in the u-v coordinatesystem by these same coordinate values, having differing locations. Thisis illustrated in FIG. 2 by two example points P₁ and P₂. Point P₁ isdefined by the coordinate values x₂, y₁, while point P₂ is defined bythe coordinate values u₂, v₁. Despite the same numerical values for x₂and u₂ as well as for y₁ and v₁, a distinct positional interval resultsfor points P₁, P₂. But without the deviations mentioned (center shift,twisting, scaling difference), points P₁, P₂ would coincide.

FIG. 3 explains an embodiment example of a method to determinedeviations between two coordinate systems of different technicalsystems. In the specific example case, reference is made to coordinatesystems used by control unit 22 and scanner 18 on the one hand and eyetracker 24 on the other hand.

First, the eye tracker 24 investigates a test object 26, which isappropriately placed essentially at that position in device 10 at whichthe eye 12 to be treated later is located. Especially the test object 26is so placed that it is in the focal plane of laser beam 16.

In the example shown, test object 26 has a flat top side 28, whichroughly in the middle has a reference pattern 30 that stands outoptically from the surrounding area. Reference pattern 30 is modeled asa pupil and correspondingly is formed by an approximately pupil-sizedcircular pattern preferably filled with color. The circular pattern 30does not of necessity have to be exactly circular; it can also have moreor less pronounced deviations from the circular form.

The image processing software incorporated in eye tracker 24 recognizesthe pupil pattern 30 and from it computes the position of the center ofthe pattern in its u-v coordinate system. The center of the pattern inFIG. 3 is indicated by 32; it represents a reference feature in thecontext of the invention.

The eye tracker 24 transmits the u-v coordinates of the circle center 32to the control unit 22. This thereupon guides the laser source 14 andthe scanner 18 to apply a plurality of test features 34 on the top side28 of test object 26 through laser irradiation. The test features 34 aresmall circles, for example, or other geometrical shapes, that stand outoptically from the surrounding areas of the top side 28 of test object26 and are detectable by eye tracker 24. For example, generation of eachtest feature 34 may require many hundreds or even many thousands oflaser pulses to be incident.

The positions at which the test features 34 are applied, are computed bycontrol unit 22 in dependence on the u-v coordinate position of thecircle center 32 communicated by eye tracker 24. A preset generationrule determines at which x,y positions the test features 34 are to beapplied with reference to circle center 32. An example of a generationrule may specify that four test features 34 ₁. . . 34 ₄ are to beapplied in a rectangular array about circle center 32, with circlecenter 32 forming the center of the rectangle. Such a rectangular arrayof four test features 34 is shown as an example in FIG. 3. Therectangular array there is approximately a square array.

In the example case shown in FIG. 3, it can be perceived that theapplied test features 34 in fact are not centric to circle center 32,but rather have a square center 36 that is displaced vis-à-vis circlecenter 32, defined as the crossing point of two square diagonals. Theoffset between circle center 32 and square center 26 allows one toconclude there are deviations between the u-v coordinate system of eyetracker 24 and the x-y coordinate system of control unit 22 and ofscanner 18. This is because in the case of such deviations, two pointswith the same numerical coordinate values in the u-v coordinate systemand in the x-y coordinate system diverge, as is made clear in FIG. 2 bypoints P₁ and P₂. A point in the x-y coordinate system with the samecoordinate values as the circle center 32 therefore is not spatiallycongruent with circle center 32, but rather is displaced from it. Sincethe test features 34 are generated with reference to this (displaced)point in the x-y coordinate system, they are centric to this point, butnot centric to the circle center 32.

For quantitative detection of the deviations between the two coordinatesystems the test object 26 provided with test features 34 is againscanned by eye tracker 24, to determine the u-v coordinates of the testfeatures 34 in the u-v coordinate system. From the u,v coordinates ofthe test features 34, u-v coordinates of the square center 36 arecomputed in addition. Square center 36 represents a derived feature inthe context of the invention, because it is derived from the testfeatures 34.

Based on the u,v positions of the test features 34 thus determined andof the square center 36, information is determined by control unit 22which characterizes the deviations between the u-v coordinate system andthe x-y coordinate system.

Specifically, the u-distance and the v-distance of the square center 36from circle center 32 permit determination of a displacement vector thatcharacterizes the extent and direction of deviation in position of theorigins of the coordinate systems. According to one example, the controlunit then computes for at least one pair of test features 34 assigned,initially-corrected u,v positions which are displaced vis-à-vis the testfeature 34 concerned by the displacement vector. The initially correctedu,v positions are consequently centered vis-à-vis circle center 32. Forexample, in FIG. 3, for the test features 34 ₁, 34 ₂ suchinitially-corrected u,v positions 34 ₁′, 34 ₂′ are drawn in, which areshifted vis-à-vis test feature 34 ₁ and 34 ₂ respectively, to the samedegree that the square center 36 is shifted vis-à-vis circle center 32.

The relative twisting of the two coordinate systems can for example bedetermined by the control unit 22 determining target coordinatepositions in the u-v coordinate system for the same pair of testfeatures for which it has determined the initially corrected u,vpositions. For this it applies the above-mentioned generation rule forthe test features in the u-v coordinate system with reference to the u,vcoordinate position of circle center 32. For example, in FIG. 3, thetarget position thus determined of test feature 34 ₁ is drawn in at 34 ₁^(s) and the target position of test feature 34 ₂ is drawn in at 34 ₂^(s) in the u-v coordinate system.

A twisting of the coordinate systems can easily be determined bycomparing the connecting straight line of target coordinate positions 34₁ ^(s) and 34 ₂ ^(s) with the connecting straight line of the initiallycorrected u,v positions 34 ₁′ and 34 ₂′. If these two connectingstraight lines are parallel, the coordinate systems are not twisted. Ifthey are at an angle to each other, the angle between the connectingstraight lines indicates the twisting angle of the coordinate systems.

To determine any scaling differences between the two coordinate systems,control unit 22, with the aid of the determined twisting angle of thecoordinate systems from the initially corrected u,v positions of thepair of test features in question, can determine the again-corrected u,vpositions, which are corrected by the twisting angle in addition to thedegree of shift. As an example, in FIG. 3 the again-corrected u,vpositions 34 ₁″, 34 ₂″ are drawn in for test features 34 ₁, 34 ₂. Theconnecting straight lines for these again-corrected u,v positions 34 ₁″,34 ₂″ now are parallel to the connecting straight lines of the targetcoordinate positions 34 ₁ ^(s), 34 ₂ ^(s).

True, the again-corrected u,v positions 34 ₁″, 34 ₂″ continue to benon-congruent with the target coordinate positions 34 ₁ ^(s), 34 ₂ ^(s).This is an indication that the axial scaling of the coordinate systemsdiffers.

By calculating the u-distance of the target coordinate positions 34 ₁^(s), 34 ₂ ^(s) and of the u-distance of the again-corrected u-vpositions 34 ₁″, 34 ₂″ and by comparison (especially quotient formation)of these u-distances, any differing scaling of the u-axis of the u-vcoordinate system and of the x-axis of the x-y coordinate system can berecognized and determined quantitatively. The same holds true for anydifferent scaling of the v-axis and of the y-axis which can berecognized and quantitatively determined by calculating the v-distanceof the target coordinate positions 34 ₁ ^(s), 34 ₂ ^(s) and thev-distance of the again-corrected u,v positions 34 ₁″, 34 ₂″ and bycomparison (especially quotient formation) of these v-distances.

Instead of the u-distance or v-distance of the target coordinatepositions and the again-corrected u,v positions of a pair of testfeatures, for determining a deviating axial scaling of the coordinatesystems, alternatively also the u-distance and/or the v-distance betweenthe target coordinate position of a test feature and the circle center32 and between the again-corrected u,v position of that same testfeature and the circle center 32 can be determined.

It is understood that a rectangular array of test features 34 is purelyexemplary and that other polygonal arrays and even a circular array oftest features 34 is readily possible.

To make it possible to optically recognize the test features 34, thearea of the surface 28 of the test object around the reference pattern30 can be printed in a color that disappears when irradiated by a laser,thereby allowing another color lying underneath to come into view. Forthis purpose, test object 26 can comprise a plate-shaped or sheet-shapedsubstrate, which has a flat printing of an underlying color on its flatsides. On this underlying color, in the area of reference pattern 30, afirst different color is printed, which forms reference pattern 30.Outside reference pattern 30, a second other color is printed that canbe bleached out by laser irradiation or removed by some other means.

In an alternative embodiment, it is conceivable to print a grid networkof fine, closely spaced lines in the area outside reference pattern 30.By local laser irradiation, the grid network can be interrupted at theirradiated locations, for example in using a color for the grid networkthat can be bleached out by laser action or by the laser generating acrater in the top side 28 of test object 26. The interruption in thegrid network thus generated can be recognized by suitable imageprocessing software and used as a test feature.

The device 10 can carry out the above-mentioned method for determiningdeviations between the u-v and the x-y coordinate systems in fullyautomatic fashion, as soon as a user inserts test object 26 and gives anappropriate start command. Especially the control unit 22, as part ofsuch an automatic calibration, can determine suitable correctionparameters for the coordinate transformation from the u-v coordinatesystem into the x-y coordinate system, and store them in a memory devicewhich is not depicted in any greater detail.

1. Method for determining deviations between coordinate systems ofdifferent technical systems, comprising determination of a coordinateposition of a reference feature (32) of a test object (26) in thecoordinate system (u,v) of a first (24) of the technical systems,attachment of at least one test feature (34) to the test object, withthe test feature being attached in the coordinate system (x,y) of asecond (18, 22) of the technical systems at a coordinate position thatis determined in dependence on the determined coordinate position of thereference feature, determination of a coordinate position of the atleast one test feature and/or at least one feature (36) derived from itin the coordinate system (u,v) of the first technical systemdetermination of deviations between the coordinate systems of the firstand second technical system, at least on the basis of: (a) thedetermined coordinate position of the at least one test feature and/orof the at least one feature derived from it in the coordinate system(u,v) of the first technical system and (b) the coordinate position ofthe reference feature in the coordinate system (u,v) of the firsttechnical system.
 2. Method according to claim 1, wherein the deviationsbetween the coordinate systems of the first and the second technicalsystem are further determined on the basis of a target coordinateposition of at last one feature among the testing and derived featuresin the coordinate system (u, v) of the first technical system.
 3. Methodaccording to claim 1 or 2, wherein multiple test features (34) areattached at various locations of the test object (26).
 4. Methodaccording to claim 3, wherein at least a part of the test features (34)are attached in a polygonal array, for example a rectangular array,around the reference feature on the test object.
 5. Method according toclaim 4, wherein as a derived feature a polygonal center (36) of thetest feature arrayed as a polygon is determined and in the coordinatesystem (u, v) of the first technical system a deviation is determinedbetween the coordinate position of the reference feature (32) and thecoordinate position of the polygon center.
 6. Method according to one ofthe foregoing claims, wherein the target coordinate position of a testfeature (34) is determined in the coordinate system (u, v) of the firsttechnical system in accordance with a coordinate distance preset forthis feature from the reference feature (32) in the coordinate system(x, y) of the second technical system.
 7. Method according to one of theforegoing claims, wherein the first technical system comprises a motiontracking device (24) with a camera directed toward the test object,wherein the motion tracking system determines the coordinate position ofthe reference feature (32) and of the at least one testing and/orderived feature (34, 36) in a first coordinate system (u, v).
 8. Methodaccording to claim 7, wherein the test object (26) bears a pattern (30),the center of which is determined by the motion tracking device as areference feature (32).
 9. Method according to claim 8, wherein thepattern (30) is a flat pattern that contrasts optically vis-à-vis thesurrounding area.
 10. Method according to claim 9, wherein the pattern(30) possesses a round contour, especially a circular or ellipticalcontour.
 11. Method according to one of claims 7 to 10, wherein thesecond technical system comprises a laser device, which attaches the atleast one test feature (34) by means of a laser beam (16), especially apulsed laser beam, to the test object (26), wherein the laser deviceuses a second coordinate system (x, y) for positioning of the laserbeam.
 12. Method according to claim 11, wherein for attachment of a testfeature (34), the test object (26) is treated by the laser beam (16) sothat the test object undergoes a local color change and/or a localcratering.
 13. Method according to one of the foregoing claims, whereinthe at least one deviation determined is used for correction ofcoordinate data, which the second technical system receives, transmittedfrom the first technical system.
 14. Test object for use in a methodaccording to one of the foregoing claims, wherein the test object (26)possesses a pattern (30) that stands out optically and at least in onearea around the pattern is configured so that through local laserirradiation, test features that stand out optically can be generated.15. Test object according to claim 14, wherein the pattern (30) is anareal pattern, preferably modeling a human pupil, which appears in afirst color, whereas the test object appears in an area around thepattern in a second color.
 16. Test object according to claim 14 or 15,wherein the test object (26) is configured to be plate- or sheet-shaped.17. Device for laser-surgical ophthalmology, comprising a laser device(14, 18, 20) to make available a pulsed focused laser beam and to directsame toward an eye (12) to be treated, an eye-tracker (24) for detectingeye movements, a control unit coupled (22) with the eye-tracker, whichis furnished to control the laser device in dependence on the detectedeye movement, wherein the control unit is additionally furnished for:(i) Carrying out a method of the type according to one of claims 1 to13, to determine deviations between a first coordinate system (u, v)used by the eye-tracker and a second coordinate system (x, y) used bythe laser device, and (ii) to allow for determined deviations with thecontrol of the laser device.